A common question people ask with the threat of military action and possible chances of World War 3 is can they get out of the draft or military service if they have flat feet. Obviously you maybe able to find a Podiatrist to make flat feet seems worse than they are. Heck, Donald Trump was able to avoid military service because of foot related issues. But here is the thing. Flat feet can be cured with a simple surgery, so the chance of you avoiding service over them are low. The military will just tell you to get some orthotics and take care of the flat feet.
Again, I know 20-25 years ago you could get out of military service of the draft for having flat feet but that was then and this is now. Much more is known and much research down. If you have flat feet you can be in the military. Sorry for bringing the bad news.
Now if you are bound and determined to get out of the draft or military, good news! Somebody wrote a book about all your options. Read it. Maybe the solution lies in there.